Compass and Straightedge

Key idea

Bisect angles, draw perpendiculars and regular polygons.

In depth

Classical constructions use only an unmarked ruler and a compass. Key ones are the perpendicular bisector, angle bisector, and equilateral triangle. They are justified by congruent triangles and show geometric reasoning without measurement.

Worked example

To bisect a segment, draw arcs of equal radius from both ends; the line through the two intersections is its perpendicular bisector.

Real-world uses

• Historical drafting
• Drawing exact regular shapes for design without a protractor

Common mistake

Changing the compass setting between arcs when the method requires it to stay fixed.

How to learn this

1. Read the key idea and say it in your own words.
2. Work through the worked example, then try a similar problem.
3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

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Related advanced topics in Geometry

• Heron’s Formula – Triangle area from three sides.
• Regular Polygon Area – Use apothem and perimeter.
• Arc Length of a Circle – Part of the circumference.
• Sector Area – Part of the circle’s area.
• Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
• Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.